Question

Find the value of ${\left(\frac{243}{32}\right)}^{\frac{3}{5}}\times {\left(\frac{2}{3}\right)}^{-3}\times \left[{\left(\frac{125}{27}\right)}^{\frac{2}{3}}\right]$.

Answer 1

${\left(\frac{243}{32}\right)}^{\frac{3}{5}}\times {\left(\frac{2}{3}\right)}^{-3}\times \left[{\left(\frac{125}{27}\right)}^{\frac{2}{3}}\right]={\left({\left(\frac{3}{2}\right)}^5\right)}^{\frac{3}{5}}\times {\left(\frac{2}{3}\right)}^{-3}\times {\left[{\left(\frac{5}{3}\right)}^3\right]}^{\frac{2}{3}}={\left(\frac{3}{2}\right)}^3\times {\left(\frac{3}{2}\right)}^3\times {\left(\frac{5}{3}\right)}^2=\frac{3^{3+3-2}\times 5^2}{2^{3+3}}=\frac{81\times 25}{64}=31.64$